Report CCG 71-57, NBS 2210472

NBS IR 74-476 '/t^ ^

Stable Pressure Transducer

J, E, Colwell

Pressure and Vacuum Section

Heat Division

National Bureau of Standards

Washington, D.C. 20234

Annual Report for Period July 1973 - June 1974

Prepared for CCG-Army/Navy/AF

July 1974

Abstract

This report describes the continuing development of a capacitive pressure

transducer which utilizes a solid dielectric material. A way of combating the

pronounced temperature dependence of this device, based on the use of materials

that have the same temperature dependence but different pressure dependences

in opposite arms of the measuring bridge, is discussed. It is proposed that

particular cuts from anisotropic materials be used to get the proper capacitive properties for tJje gauge. The thermal relaxation phenomena and pronounced

temperature gradients observed in the pressure vessel are described. The

design of the capacitance bridge and automating circuitry to be used with the

capacitance pressure gauge is presented.

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1

INTRODUCTION

The objective of this project is to develop a pressure transducer which

can be used as a transfer standard in disseminating the absolute pressure

values determined by controlled clearance piston gauges in standards laboratories. We are currently interested in pressures up to 70 or 140 MPa (10,000

or 20,000 psi), a range where the stated accuracy of the piston gauges is of

the order of 1:10**. .The pressure transducer should therefore be capable of

precision in excess of 1:10^ over this range but another requirement of a

transfer standard is that it will be able to maintain its calibration for an

extended period of time while in constant use. The latter requirement has led

to the idea of a capacitance gauge using a solid dielectric capacitor. Such

a device using a hard, and preferably crystalline, dielectric material with

electrodes deposited directly on its- surf ace would not be expected to suffer

any perminent deformation with repeated cycling under hydrostatic pressures

and would therefore have the required long term stability, Andeen, Fontanella,

and Schuele have demonstrated the feasibility of such a gauge using single

crystals of CaF2 as a dielectric medium. With this gauge capacitance changes

of about 3:10^ must be resolved to determine pressures to a precision of

1:10*^ at 70 MPa, Using the three terminal method, modern A.C, bridge techniques and accurate ratio transformers, capacitance measurements to 1:10'' are

readily achievable. Tests have not indicated any instabilities in the capacitors,

so a gauge using CaF2 crystals does meet the basic requirements. The capacitance

of the CaF2 gauge is, however, strongly temperature dependent; 1 mK changes the

capacitance by 3:10 , the required resolution of the gauge. It is possible to

thermostat the gauge within the 1 mK range but it is not convenient and only

transfers the long term stability requirements to the thermostating thermometry.

2

The problem is compounded by the considerable amount of heat which is generated

in the pressure vessel whenever the pressure is changed thus requiring long

periods to reestablish thermal equilibrium. A search has been made for materials

having a smaller temperature to pressure dependence of capacitance but no dramatic

improvements have been found. The search is continuing in this laboratory but the

nature of the measurements make this process tedious. As an expedient, toward

getting a working device, other ways of overcoming the temperature dependence of

the capacitance measurement are being sought. The bridge method required for the

capacitance measurements offers other ways of cancelling out the temperature dependence of the pressure determination. One technique is to put capacitors of the

same material in opposite sides of the bridge so that their capacitances are

cancelling each other. If one capacitor is pressurized and the other kept at

ambient pressure while keeping the two. in thermal contact, the temperature dependence will cancel to first order and any additional thermostating required

should be trivial. James Miller of the U.S. Army Missile Command is pursuing

developments along this line. The principle difficulty of this method is that

it requires establishing thermal equilibrium between a sample within a pressure

vessel and one outside which can require a considerable length of time. In our

laboratory we are currently concentrating on a variation of this same general

idea. We are attempting to find two materials which will have the same temperature dependence of capacitance yet having considerably different pressure

dependencies. Again, the capacitors would be placed in opposite arms of the bridge

but both would be inside the pressure vessel. In this way, the temperature dependence of the device would cancel as above but the two capacitors could be in

intimate thermal contact, thereby reducing the thermal equilibation time between

them. To utilize this technique we are now faced with the problem of finding the

3

two materials with the proper capacitive properties. Since several anisotropic

materials have considerably different temperature dependence along the different

crystalline axes we are hoping that we will be able to match two samples by

cutting a sample from the anisotropic crystal at an intermediate angle between

the major axes.

Toward this end we have begun collecting data on anisotropic material and

are continuing to look at various other materials that may be of possible use

in the device. Several experiments have been carried out to gain knowledge

about the thermal equilibration problems within pressure vessels. Work on the

prototype capacitance bridge for use with a capacitive pressure transducer is

described,

SAMPLE ELECTRODES AND SAMPLE HOLDERS

The deposition of electrodes on the dielectric samples has been a problem

throughout this work both from the standpoint of forming the insultaing gaps for

the guard electrodes and because of poor adherence of the electrodes to the sample. For several months we have been using vacuum deposited aluminum coatings

exclusively. Samples are cleaned by washing with soap and water, rinsing with

alcohol and freon, and finally ion bombarding in the evaporator for upwards to

1 hour prior to coating. We have started using 99.999% aluminum wire as our

source material. This wire outgasses very little on melting so that a good

vacuimi can be maintained throughout the coating process which probably accounts

for the excellent mirror-like coatings obtained. All coatings are checked by

pulling with Scotch tape and very few have failed the test.

We are continuing to form the electrode gaps by masking the samples with

wedge-shaped steel rings during the deposition process. Magnets behind the

sample support in the evaporator are used to hold both the sample and masking

4

ring In place. We are using hardened steel for the masking rings which makes

them much less susceptible to damage than the mild steel rings formerly used.

In addition it is possible to lap a much finer edge on the hardened steel rings

so that we have been able to consistently achieve gaps as narrow as 8 ym (0.0003").

One drawback in using masking rings with a fixed source and a fixed sample

is that there is invariably some area of the sample that is shadowed sufficiently

by the ring that the coating is quite thin. We have overcome this problem by

adapting the evaporator so that the sample is rotated about its axis during the

evaporation process. The evaporator filament is positioned, so that it is at a

45" angle to the sample axis, in this way all areas in the vicinity of the ring

get a uniform coating. A disadvantage of this procedure is that only one

sample can be coated at a time thus greatly increasing the sample preparation

time.

The sample holders for mounting the dielectric samples in the pressure

vessel have been modified so that electrical contacts are made with small

gold-plated nickel deposited bellows, see Fig. 1. The bellows are 1/8"

diameter and 3/16" long and can be compressed up to 0.070", The advantage

in using the bellows is that their spring constants are very consistant

(2,3g/0.001") so that the force on the contacts can be predetermined by adjusting the amount the bellows will be compressed when the sample holder is

assembled. This adjustment is made by varying the thickness of the Teflon

washers which insulate the contacts from the body of the sample holder. The

bellows of the high voltage contact is usually compressed about 0.040" (92 g

load) and that of low voltage contact 0.020" (46 g load). In this way there

is sufficient load 46 g) on the -sample to ensure that good electrical contact

between the guard ring of the sample and the grounded case of the sample holder

5

is maintained. With this arrangement we have had no trouble with contacts

opening during pressure cycling,

SAMPLE SELECTION

In our continuing survey of the temperature and pressure dependence of

capacitance of various materials we have been concentrating on materials that

are mechanically hard and chemically inert, have a low dielectric loss component,

and are available in an appropriate form. An additional qualification to the

last condition must be a reasonable cost, which does keep the number of materials

to be tested within bounds. In Table 1 we have tabulated the temperature and

pressure dependence of the capacitance of several materials for which data are

available. The third column gives the ratio of the temperature to pressure

dependence which, for our purpose, we may consider as a quality factor. As can

be seen, CaF2, which we consider our benchmark material, was not a poor initial

choice. The ratio for X-cut quartz is much better, but the magnitude of the

pressure dependence of this material is so small that the measurement sensi-r

tivity will be marginal. Pyrolytic boron nitride is by far the best of any

material studied and is still considered for possible use, but this material

has a layered structure and the surface is rather easily damaged. We have put

several anisotropic materials on the list to show the range that their temperature and pressure dependences cover. From this list there are not many combinations of materials that could be used in the opposite arms of the capacitance

bridge to achieve cancellation of the temperature dependence. The one attractive

pair is the a-cut paratellurite (Te02) and an intermediate cut, probably about a

45", of sapphire (AI2O3) , This combination would have a pressure sensitivity

approximately equal to CaF2. To look for other combinations we are preparing

6

Table 1

The Temperature and Pressure Dependence of the Capacitance

of Select Materials

Material

3T

p

10l2/Pa

3P

T

(3C/9T) MPa

(3C/9P) K

CaF2 263 - 38 - 6.9

BaF2 231 - 50 - 4.6

NaCl 356 -118 . - 3.0

TlBr -330 -218 1.51

6N - 52 123 - 0.42

KTaOa -2700 -182 15.0

SrTi03 -3820 -248 15.4

Quartz-fused .11 4.6 2.4

Quart z-Z-cut 30 - 1.7 -17.6

Quart z-X-cut 10 9.5 1.05

Al203-a 110 - 10 -11

AI2O3-C 190 - 11 -17

Ti02-a -650 - 35 18.5

Ti02-c -990 - 72 13.8

Te02-a 156 29 5.4

Te02-c 244 - 49 - 5.0

MgO 111 - 20 5.5

CaCOs-a (400)

CaCOs-c (400)

7

to look at MgF2 and CaCOs, and to reexamine Quartz, AI2O3, and Te02. We are

going to measure isotropic materials such as, gadolinium gallium 'garnet

,

magnesium aluminate spinel, and several glasses to try fo find other cases where

the temperature dependence of the material will fit within the range of an

anisotropic material.

We have repeated, with new samples, the earlier measurements on quartz

made in this laboratory. The equilibritm temperature and pressure dependences

measured were close to the earlier values, but a strange relaxation phenomenon

was observed. When the pressure was changed and the thermal equilibrium had been

reestablished in the pressure vessel, there still occurred a very long relaxation process which required up to 24 hours before equilibrium was reached. In

changing the pressure between 0 and 70 MPa, the total relaxation was about 40%

of the total-initial change and always back toward its previous equilibrium

value. The effect was largest in the Z-cut crystal, it was observed in 45°-cuts

containing the Z-axis, but was not noticeable in X or Y cut crystals. It is

thought that the phenomenon may be caused by the piezoelectric properties of

quartz, possibly due to charge generation on the surface of the sample when it

is pressurized. Tests, however, such as shorting the two sides of the capacitor

had no effect on measured capacitance. We have no explanation of this phenomenon

but the experience makes one wary of piezoelectric materials.

THERMAL EQUILIBRATION IN THE PRESSURE VESSEL

In the introduction we mentioned some of the thermal equilibration

problems encountered in the pressure vessel. Here we describe some observations made on our system—some were by design, others incidental to other

measurements. In Fig. 2 is pictured the group of five sample holders that

8

are usually used in a pressure run. They are mounted on the pressure vessel

closure through which the electrical leads are brought. This assembly fits

inside a pressure vessel which is 1 1/2" I.D, and 3 5/8" O.D. The well in

the vessel is 15" deep so that it is only half filled by the sample assembly;

the lower half has been filled with a brass cylind-er to reduce the oil volume

in the system. In operation the pressure vessel is immersed in a thermostated

water bath.

It is interesting, first of all, to calculate the temperature changes

which occur in the system when it is pressurized. If we had an instantaneous,

i.e. adiabatic, compression of the system to 70 MPa 0-0,000 psi) the oil in

the system would undergo the largest change, warming some 7 to 10 K. The

brass sample holders (and brass cylinder) would warm about 0.4 K. The steel

vessel uniformly cools about 0.09 K under the combined influence of hoop and

longitudinal stretching and radial compression. The sample itself undergoes

a temperature change which would be superimposed in the observed capacitance

change due to the pressure increase—in CaF2 the instantaneous temperature

increase would be 1.15 K.

It is possible to solve the expressions for the thermal relaxation of such

a system but hardly practical. We can write an approximate relationship for

the relaxation which should be useful for discussion purposes,

T - T

XA

log J-TT = ^

CVp5,

t + Y. (1) o e

In this expression T is the temperature at time t, T^ and T^ are the equilibrium

and arbitrary initial temperatures. X and Y are constants which depend on the

geometry, X, A, and I axe the thermal conductivity, cross sectional areas, and

9

conductance path length of the component of the system which impedes conduction

the most, whereas C, V, and p are* the specific heat, volume, and density of the

component with the largest heat capacity.

Upon compression, the oil in the system produces about an order of magnitude more heat than the solid components and is al«o the poorest conductor so

it is obvious from the start that its volume should be minimized. It is also

apparent that for any given geometry the relaxation time will increase as the

square of the overall size.

In our apparatus, pressurizing to 70 MPa (in approximately 1 minute) raises

the temperature of the samples between 1 and 2 K. The system takes about 45

minutes to return to equilibrium (i.e to within 1 mK of the thermos tated temperature) showing a relaxation time of 5-6 minutes. With the brass cylinder in

the pressure vessel the amount of heat produced is cut in half but the relaxation

time is slightly longer so that it takes the same length of time to reach

equilibrium.

We are currently interested in how quickly two samples within the pressure

vessel will equilibrate, two experiments were carried out for this purpose. In

the first, two CaF2 samples, each mounted in individual sample holders, were

placed adjacent to each other in the pressure vessel assembly. The sample holders

were firmly bolted together by nuts on the screw rod supports so they would

normally be considered to be in intimate thermal contact. The experiments were

run with the CaF2 samples in opposite arms of the capacitance bridge so that the

capacitance difference was observed. Upon pressurizing the system to 70 MPa large

temperature gradients were set up between the two cells. The capacitance change

reached 80 ppm (equivalent to a temperature difference of 0.3 K) and took 35

minutes to relax to the equivalent of 1 mK difference between the samples. On

10

decompression the behavior was different in one respect, the maximum

displacement (in the opposite direction) was only 40 ppm but it relaxed back

through zero displacement and approached equilibrium from the opposite side.

The total equilibration time was again 35 minutes. Heating the pressure

vessel via the thermos tating water bath at a rate of 0.5K/min produced a

steady state capacitive difference of 12 ppm (equivalent to 50 mK)

In an attempt to minimize the temperature gradients observed in the above

system, the double sample holder shown in Fig. 3 was fabricated and the same

set of experiments were carried out. The results showed a large improvement

but not as much as one would expect. On compression to 70 MPa the capacitance

difference reached 3,5 ppm (14 mK) but took 15 minutes to return within 1 mK

of equilibriim. On decompression (the displacement was in the same direction)

the difference reached 3 ppm and took 9 minutes to return to equilibrium. Upon

heating at l/2K/min the displacement reached 0,8 ppm.

It is obvious from these experiments that temperature gradients within a

pressure cell can be very pronounced. In order to bring two samples into

thermal equilibrium we can improve their thermal contact. Two samples in the

bridge network could be physically joined at their common low voltage contact.

Another approach would be to make the environment within the pressure cell

symmetrical, so that the same gradients exist at both samples.

One result of these two experiments was a demonstration of the precision

possible with the capacitance gauge. In comparing the two capacitors after

thermal equilibration was attained, the ratio of capacitance was the same to

within our limit of detection, 5:10^, for pressures from 0 to 140 MPa. This

was true in both experiments although there was a difference of 3 ppm in the

capacitance ratio between the two experiments. In both experiments there was a

change in the ratio of about 0,8 ppm on changing the temperature from 20 to 40 °C,

11

AUTOMATIC CAPACITANCE BRIDGE

A limited-range capacitance bridge is being constructed which was designed

specifically for use with the dielectric capacitance pressure gauge. It will

be capable of measuring the ratio of two capacitors which differ by less than

10% and which also have reasonably small loss tangents. After an initial

adjustment, using a phase compensated resistor, the bridge is intended to be

completely automatic.

The design of the bridge proper, shown in Fig. 4, is in principle the

same as that presently being used as a research tool in our laboratory. The

bridge transformer forms the 1:1 ratio arm of the bridge and supplies the voltage

for the ratio transformer used in balancing the bridge. The output voltage of

the ratio transformer is injected into one of the ratio arms of the bridge

through the two stage transformer. The power for this injected voltage comes

from an operational amplifier so that there is no loading of the ratio transformer and the bridge impedance is kept small. It is the turns ratio on the

two stage transformer and the voltage supplied to the ratio transformer that

limits the range of capacitor ratios that can be measured. A switch on the

primary of the two stage transformer allows the selection of a total range of

either 1 or 10%. The switch on the input to the ratio transformer allows this

range of bridge ratios to be taken on either the positive or negative sides or

centered about the ratio of 1. Any difference in loss between the measuring

capacitor and the reference capacitor is compensated by injecting an in-phase,

i.e. resistive component, signal into the detector arm of the bridge. The

magnitude of this signal is controlled by multiplying the D.C. in-phase signal

of the phase sensitive detector by an A.C. signal from the bridge transformer.

12

The exact phase alignment of the bridge will be manually adjusted by balancing

out the signal from a pure resistance.

Fig. 5 is a block diagram of the logic circuitry as presently planned for

the automation of the capacitance bridge. The design is limited to some extent

by the incorporation of a 5 decade programmable ratio transformer (PRT) . We

require a 7 digit reading and would desire 8 digits, so it is necessary to limit

the range of capacitance ratios that the instrument can cover. In the 1% range

the first two significant digits are preset by the range control, in the 10%

range only the first significant digit is preset. The next five significant

digits are determined by the ratio transformer and two additional digits are

obtained by the digital conversion of the analog voltage resulting from any

remaining bridge imbalance.

In operation the imbalance current from the capacitance bridge is amplified

by an FET preamplifier and by three programmable gain amplifier sections. These

are followed by two lock-in amplifiers, one phased to detect the resistive loss

component of the bridge and the other phased at 90° to detect the capacitive

imbalance. The rectified loss component is further filtered and used to control

the automatic loss feedback network in the bridge. This signal can be monitored

by a front panel meter.

The rectified capacitance imbalance signal is fed to the gain control module

and to two voltage-to-frequency converters (VFC) . The signal is inverted before

one of the VFC's, so that one VFC delivers a pulse rate proportional to positive

signals and the other to negative signals.

The output of the two VFC's are fed into a bank of 14 up-down counters by

way of a multiplex unit that switches in and out various counters. After each

period of counting the contents of the counters are dumped into latches with

13

hold that count while the next is in progress. The signals from the latches

are routed through buffers to the BCD output for external processing and are

routed to the seven-segment decoders which generate a 10 digit LED display. The

signal from latches 4', 5, 6, 7, and 8 are routed through drivers to the programmable ratio transformer and provide the updated bridge setting. Only

decades 9 through 13 are zeroed before each count so that the new count is

added to or subtracted from the existing transformer setting.

The clock steps down the bridge frequency to approximately 10 second and

1 second intervals which are used as counting times. The clock is used to turn

the counters on and off, and while the counters are off enables the gain control

and range control, transfers information from the decade counter to the latches,

zeros counters 9 through 13 and turns on the counters for the next interval.

The gain control looks at the output of the bridge and sets the amplifier

gain decades to keep the input to the VFC's less than 10 volts but greater than

1/2 volt. It is operative only when the counters are off. When the amplifier

gain changes the counting gain or count time must change to keep the overall

gain constant. The counter gain is changed by the multiplexers switching between the last five decade counters. On the highest amplifier gain the clock

is set for 10 second counts; on all other gains it is set for 1 second counts.

The range control switches between the following deviation capabilities of

the bridge: 0 to 1%, + 1/2%, -1 to 0%, 0 to 10%, + 5%, and -10 to 0%. The

switching is done automatically seeking the highest sensitivity, but can be

set manually. Range control switching takes place only when the counter is

off and only when the programmable ratio transformer is asked to go beyond its

limit (as detected by a carry of borrow signal from counter 4'). Counters 1

2, 3, 4, 4' are reset each time a range control switching occurs.

14

Decade counters 9 and 10 do not control the bridge. They are zeroed before

each count and provide the two analog decades of bridge sensitivity beyond the

ratio transformer setting.

The fourth decade is split, 4 going to the readout and 4' controlling the

PRT. This was necessary to permit the use of the bridge ranges + 1/2% and

+5%. On these ranges, when the bridge ratio (and readout) is exactly 1,000,

the PRT must be set to 50000, the 5 appearing in the fourth readout decade.

The precision desired from this bridge, 1:1(7 , is pushing the limits of

the programmable ratio transformer. These devices are frequency dependent, the

ratios depending to some extent on winding impedance,- core size, shunt capacitance,

etc.. The ratio transformer was designed for 400 Hz operation but we would like

to work at a higher frequency and had intended to use 1592 Hz (w = 10*^) , the

frequency of our research bridge. We have had the NBS Electrical Measurements

Section determine the accuracy of the ratio transformer as a function of frequency to establish the size of the errors involved; the results are shown in

Fig. 6. Ratio settings of 0.2, 0.5, and 0.8 are plotted versus frequency squared.

Theoretically, errors in ratio settings reach maxima at the 0,2 and 0,8 settings

plotted in the figure.

We have decided to operate the bridge at 1,000 Hz where the accuracy of

all ratios is within 2:10^, and, in addition, the ratios all err in the same

way except for the two lowest settings. As a result, bridge precision of 1:10^

should be achievable.

The design of all components of the capacitance bridge has been completed

and nearly all the hardware for its construction has been assembled. The

toroidal transformers have been wound. The oscillator has been constructed and

masks for the printed circuit boards of the other components are being laid out.





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